Cost Minimization Alice owns a firm which produces oranges. Alice needs only two
ID: 1224091 • Letter: C
Question
Cost Minimization
Alice owns a firm which produces oranges. Alice needs only two types of inputs which we call capital denoted by K and labor denoted by L. Price of capital i.e. the rental rate is r and price of labor i.e. wage rate is w. The technology available to Alice can be represented by the following Cobb Douglas production function f(K, L) = KL. She chooses a combination of labor and capital denoted by L and K respectively to maximize profits. Marginal product of labor MPL = K and marginal product of capital is MPK = L. Alice wants to produce y oranges.
1. Write down the cost minimization problem faced by Alice’s firm
2. What conditions should Alice’s chosen cost minimization bundle i.e. (K, L) satisfy
3. Solve for the optimal K and L in terms of (y, w, r) 4. Write down the cost function
Explanation / Answer
can i complete this with linear programming model